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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.1.g.a $2$ $0.190$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) $-$ \(q+\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}+q^{11}+\cdots\)
380.1.o.a $2$ $0.190$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) $-$ \(q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
380.1.x.a $4$ $0.190$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(2\) \(0\) $-$ \(q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
380.2.a.a $1$ $3.034$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\)
380.2.a.b $1$ $3.034$ \(\Q\) None None \(0\) \(2\) \(-1\) \(2\) $-$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
380.2.a.c $2$ $3.034$ \(\Q(\sqrt{2}) \) None None \(0\) \(-4\) \(2\) \(-4\) $+$ \(q+(-2+\beta )q^{3}+q^{5}+(-2-2\beta )q^{7}+\cdots\)
380.2.a.d $2$ $3.034$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(4\) $-$ \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)
380.2.c.a $4$ $3.034$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
380.2.c.b $6$ $3.034$ 6.0.14077504.2 None None \(0\) \(0\) \(-1\) \(0\) $-$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
380.2.d.a $16$ $3.034$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots\)
380.2.d.b $40$ $3.034$ None None \(0\) \(0\) \(-4\) \(0\) $-$
380.2.f.a $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(-20\) \(0\) $-$ \(q-\beta _{12}q^{2}+\beta _{10}q^{3}+\beta _{16}q^{4}-q^{5}+\cdots\)
380.2.f.b $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(20\) \(0\) $-$ \(q-\beta _{15}q^{2}+\beta _{9}q^{3}-\beta _{19}q^{4}+q^{5}+\cdots\)
380.2.i.a $2$ $3.034$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(-8\) $-$ \(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-4q^{7}+\cdots\)
380.2.i.b $6$ $3.034$ 6.0.1783323.2 None None \(0\) \(1\) \(3\) \(4\) $-$ \(q+(\beta _{3}-\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
380.2.i.c $8$ $3.034$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-1\) \(-4\) \(0\) $-$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
380.2.k.a $2$ $3.034$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(-4\) $-$ \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
380.2.k.b $2$ $3.034$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(-4\) \(4\) $-$ \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
380.2.k.c $52$ $3.034$ None None \(-2\) \(-2\) \(4\) \(-4\) $-$
380.2.k.d $52$ $3.034$ None None \(2\) \(2\) \(4\) \(4\) $-$
380.2.l.a $8$ $3.034$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-6\) $-$ \(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b $12$ $3.034$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(4\) \(4\) $-$ \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
380.2.n.a $40$ $3.034$ None None \(-3\) \(0\) \(20\) \(0\) $-$
380.2.n.b $40$ $3.034$ None None \(3\) \(0\) \(-20\) \(0\) $-$
380.2.r.a $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(1\) \(0\) $-$ \(q+(\beta _{1}-\beta _{11})q^{3}+(-\beta _{7}+\beta _{13})q^{5}+\cdots\)
380.2.s.a $112$ $3.034$ None None \(0\) \(0\) \(-2\) \(0\) $-$
380.2.u.a $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(3\) \(0\) \(0\) $-$ \(q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
380.2.u.b $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(3\) \(0\) \(0\) $-$ \(q+\beta _{13}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
380.2.v.a $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(-4\) \(6\) \(-2\) \(0\) $-$ \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(2\) \(-6\) \(-2\) \(0\) $-$ \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c $216$ $3.034$ None None \(0\) \(0\) \(0\) \(0\) $-$
380.2.y.a $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(2\) \(-8\) $-$ \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
380.2.y.b $36$ $3.034$ None None \(0\) \(-6\) \(-4\) \(4\) $-$
380.2.bb.a $336$ $3.034$ None None \(0\) \(0\) \(-12\) \(0\) $-$
380.2.bd.a $60$ $3.034$ None None \(0\) \(0\) \(0\) \(0\) $-$
380.2.be.a $120$ $3.034$ None None \(-3\) \(0\) \(0\) \(0\) $-$
380.2.be.b $120$ $3.034$ None None \(3\) \(0\) \(0\) \(0\) $-$
380.2.bh.a $120$ $3.034$ None None \(0\) \(0\) \(0\) \(6\) $-$
380.2.bj.a $672$ $3.034$ None None \(-12\) \(0\) \(-24\) \(0\) $-$
380.3.b.a $72$ $10.354$ None None \(4\) \(0\) \(0\) \(0\) $-$
380.3.e.a $12$ $10.354$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $-$ \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(-1+\beta _{6}-\beta _{11})q^{7}+\cdots\)
380.3.g.a $4$ $10.354$ \(\Q(\sqrt{-6}, \sqrt{14})\) None None \(0\) \(0\) \(-20\) \(0\) $-$ \(q-\beta _{1}q^{3}-5q^{5}+\beta _{2}q^{7}+5q^{9}+4q^{11}+\cdots\)
380.3.g.b $4$ $10.354$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(0\) $-$ \(q+(2-\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{7}-9q^{9}+\cdots\)
380.3.g.c $12$ $10.354$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(12\) \(0\) $-$ \(q-\beta _{5}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)
380.3.h.a $108$ $10.354$ None None \(0\) \(0\) \(4\) \(0\) $-$
380.3.j.a $232$ $10.354$ None None \(0\) \(0\) \(-8\) \(0\) $-$
380.3.m.a $36$ $10.354$ None None \(0\) \(-4\) \(10\) \(22\) $-$
380.3.o.a $40$ $10.354$ None None \(0\) \(0\) \(-1\) \(0\) $-$
380.3.p.a $232$ $10.354$ None None \(0\) \(0\) \(-2\) \(0\) $-$
380.3.q.a $160$ $10.354$ None None \(0\) \(0\) \(0\) \(0\) $-$
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